ANALYTICAL MECHANICS respect to the time. Differentiating (3) we obtain dr = , _ ~ r dt r dt 'entiating (4) we get de (5) = y cos 6 x sin 6. components satisfy the relation 0 = Vf2+r202. (6) (7) ILLUSTRATIVE EXAMPLE. Article describes the motion defined by the equations x a cos kt, (a) y = a sin kt. (b) .e equation of the path, the velocity at any instant, and the com-i of the latter. .ring and adding (a) and (b) we eliminate t and obtain x* + ?/ = a2 equation of the path. Teutiating (a), we have x = ~ = ka sin kt = Joy. rentiating (b), we obtain y = dft = ka cos kt ^ = kx- FIG. 51.